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# A stick is broken into 2 pieces. One of the pieces is

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A stick is broken into 2 pieces. One of the pieces is [#permalink]  27 Mar 2006, 17:31
1. A stick is broken into 2 pieces. One of the pieces is further broken into two pieces.
What is the probability that the (three) pieces so obtained form the sides of a triangle ?
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One piece is broken into 2 pieces, lets call them x & y.

it can be done in 3 possible ways which is
x = y ; x > y ; x < y.

Inorder to form a triangle : sum of 2 sides > 3rd side and difference of 2 sides < 3rd side. So 2 events x > y or y > x can produce the desired results. Therefore Prob of the desired event - 2/3

To form a triangle the longer piece should be further broken in to 2

Assuming x > y,
If x is further broken into x1 & x2 then the possible events can be
x2 - x1 = y ; x2 - x1 > y; x2 - x1 < y. what we need is x2 - x1 < y. Therefore 1/3.

So final answer is 2/3 * 1/3 = 2/9.

A Sincere try. Hope I got it right
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